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Theorem sslin 3308
 Description: Add left intersection to subclass relation. (Contributed by NM, 19-Oct-1999.)
Assertion
Ref Expression
sslin (𝐴𝐵 → (𝐶𝐴) ⊆ (𝐶𝐵))

Proof of Theorem sslin
StepHypRef Expression
1 ssrin 3307 . 2 (𝐴𝐵 → (𝐴𝐶) ⊆ (𝐵𝐶))
2 incom 3274 . 2 (𝐶𝐴) = (𝐴𝐶)
3 incom 3274 . 2 (𝐶𝐵) = (𝐵𝐶)
41, 2, 33sstr4g 3146 1 (𝐴𝐵 → (𝐶𝐴) ⊆ (𝐶𝐵))
 Colors of variables: wff set class Syntax hints:   → wi 4   ∩ cin 3076   ⊆ wss 3077 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122 This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-v 2692  df-in 3083  df-ss 3090 This theorem is referenced by:  ss2in  3310  difdifdirss  3453  ssres2  4855  ssrnres  4990  sbthlem7  6861  ioodisj  9826  ntrss  12347  cnptoprest  12467
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